Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns

Abstract

We show that in {\em ballistic} mesoscopic SNS junctions the period of critical current vs. magnetic flux dependence (magnetic interference pattern), $I_c(Φ)$, changes {\em continuously and non-monotonically} from $Φ_0$ to $2Φ_0$ as the length-to-width ratio of the junction grows, or temperature drops. In {\em diffusive} mesoscopic junctions the change is even more drastic, with the first zero of $I_c(Φ)$ appearing at $3Φ_0$. The effect is a manifestation of nonlocal relation between the supercurrent density and superfluid velocity in the normal part of the system, with the characteristic scale $ξ_T = \hbar v_F/2πk_BT$ (ballistic limit) or $\tildeξ_T = \sqrt{\hbar D/2πk_BT}$ (diffusive limit), the normal metal coherence length, and arises due to restriction of the quasiparticle phase space near the lateral boundaries of the junction. It explains the $2Φ_0$-periodicity recently observed by Heida et al. (Phys. Rev. B {\bf 57}, R5618 (1998)). We obtained explicit analytical expressions for the magnetic interference pattern for a junction with an arbitrary length-to-width ratio. Experiments are proposed to directly observe the $Φ_0\to 2Φ_0$- and $Φ_0\to 3Φ_0$-transitions.